On the identification of degenerate indices in the nonlinear complementarity problem with the proximal point algorithm

In this paper we focus on the problem of identifying the index sets P(x):=i|x_i>0, N(x):={i|F_i(x)>0 and C(x):=i|x_i=F_i(x)=0} for a solution x of the monotone nonlinear complementarity problem NCP(F). The correct identification of these sets is important from both theoretical and practical points of view. Such an identification enables us to remove complementarity conditions from the NCP and locally reduce the NCP to a system which can be dealt with more easily. We present a new technique that utilizes a sequence generated by the proximal point algorithm (PPA). Using the superlinear convergence property of PPA, we show that the proposed technique can identify the correct index sets without assuming the nondegeneracy and the local uniqueness of the solution.This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sports and Culture of Japan.Mathematics Subject Classification (2000): 90C33, 65K10     

Neutron activation analysis of iodine in soil

A simple pre-irradiation procedure for the separation of iodine from soil has been developed. A soil sample was heated in a quartz tube for 15 min at about 900 °C. The evaporated iodine was collected in activated charcoal, which was produced from phenol resin with low impurities. The charcoal, with sorbed iodine, was irradiated by neutrons and the¹²⁸I produced was measured. A successful elimination of the background radioactivity due to the matrix elements was possible with this separation procedure. The detection limit by this method for soil samples was about 0.1 mg/kg (dry). The method has been applied to analyze selected soil samples.     

Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Determination of129I and127I in environmental samples by neutron activation analysis (NAA) and inductively coupled plasma mass spectrometry (ICP-MS)

In order to assess the levels and behavior of¹²⁹I (half-life: 1.6×10⁷ y) and¹²⁷I (stable) in the environment, we have developed analytical procedures involving neutron activation analysis (NAA). Environmental samples collected around Tokaimura, Ibaraki Prefecture, Japan, have been analyzed using this method. Ranges of¹²⁹I and¹²⁷I concentrations in surface soil were 0.9–180 mBq kg^–1 and 1–60 mg kg^–1, respectively. Higher¹²⁹I concentrations were found in soil samples collected from coniferous forests, suggesting a contribution from tree canopies in the deposition of this nuclide. Most of the¹²⁹I in soil, was found to be retained in the first 10 cm. The¹²⁹I/¹²⁷I ratios in wheat fields were lower than those in rice paddy fields.A soil sample collected by IAEA from an area contaminated by the Chemobyl accident was also determined. The¹²⁹I concentration and the¹²⁹I/¹²⁷I ratio were 1.6 mBq kg^–1 and 1.7×10^–7, respectively. The¹²⁹I level in this sample was higher than the values obtained in areas far from nuclear facilities in Japan. It was suggested that the analysis of¹²⁹I in soils in the Chernobyl area may be useful in evaluating the¹³¹I levels at the time of the accident.Analyses of¹²⁹I and¹²⁷I by ICP-MS in water samples were also made. The analytical speed of this method was very high, i.e., 3 minutes for a sample. However, there is a sensitivity limitation for¹²⁹I detection due to interference from¹²⁹Xe with the¹²⁹I peak. The detection limits for¹²⁹I and¹²⁷I in water samples were about 0.5 mBq ml^–1 and 0.1 ng ml^–1, respectively.     

Neutron activation analysis of iodine-129 and iodine-127 in environmental samples

The possibilities of reactor induced (n, p) reactions as a tool for neutron activation analysis of titanium in geological samples are discussed. The interference of calcium and scandium is experimentally evaluated. Results for Ti, Ca and Sc in GSP-1 and PCC-1 standard rocks are presented. On the basis of the experimental values, it is concluded that the⁴⁷Ti(n, p)⁴⁷Sc reaction is the most favourable for titanium determination.     

Syntheses of fluorine-containing fused polycyclic compounds: photo-cycloaddition of indene to cyclic fluoro-olefins and some reactions concerning the adducts

Acetophenone photo-sensitized addition of indene to cyclic fluoro-olefins (1,2-dichlorohexafluorocyclopentene-1, 1,2-dichlorotetrafluorocyclobutene-1 and hexafluorocyclobutene) gave the corresponding cycloadducts in satisfactory yields. The cycloadducts obtained predominantly had exo configuration.Some reactions such as reduction, oxidation, dechlorination and halogenation, of the cycloadducts were also studied.     

Asymmetric synthesis of axially chiral benzamides and anilides by enantiotopic lithiation of prochiral arene chromium complexes

Axially chiral benzamides and anilides were prepared by enantiotopic lithiation at the distinguished benzylic methyl of prochiral tricarbonylchromium complexes of N,N-diethyl 2,6-dimethylbenzamide (1) and N-methyl-N-acyl 2,6-dimethylaniline (14 and 21) with a chiral lithium amide base followed by electrophilic substitution in good yields with high optical purity. The resulting axially chiral chromium-complexed benzamides and anilides were oxidized under air to give chromium-free axially chiral benzamides and anilides in an enantiomerically active form without axial bond rotation at room temperature.     

Application of non-thermal atmospheric pressure ac plasmas to the carbon dioxide reforming of methane

Methane conversions of 11.9%, yields of hydrogen as high as 23.3% and energy yields of 1.0 mol H₂/kWh have been achieved from CO₂ reforming of CH₄ in non-thermal, atmospheric pressure plasma reactors with Pt coated electrodes. Two reactors have been studied. A novel fan type reactor consisting of a movable rotor and immobile stator produced the highest yields in contrast to a tube type (silent discharge) reactor with a glass dielectric barrier. Conversions, yields of hydrogen and energy yields (expressed as mol H₂/kWh) were studied for CO₂/CH₄ concentrations of 1.1% and 5.0% in He as a function of flow rate and input voltage. Hydrogen yields are observed to increase as the input voltage is increased from 411 V to 911 V and the flow rate is decreased from 100 cc/min to 30 cc/min. Energy yields vary only slightly with input voltage and flow rate. Hydrogen yields show little dependence on CO₂/CH₄ concentrations, but energy yields are approximately five times greater for the 5.0% mixture than the 1.1% mixture. Selectivities to H₂, CO, coke, and low molecular weight hydrocarbons were also evaluated and compared to data obtained without CO₂ in the feed. Hydrogen selectivities of nearly 100% were obtained, with small amounts of ethane and propane as the only observed side products and the selectivites were approximately the same whether CO₂ was present or absent in the mixture. However, the reaction proceeds much more cleanly when CO₂ is present, producing CO. The syngas product has an H₂ : CO ratio of 1.5 with the fan type reactor and 0.67 with the tubular reactor. In the absence of CO₂, coke is the main carbonaceous product. Under all conditions studied the fan type reactor demonstrated higher methane conversions (up to 11.9%) and selectivities to hydrogen.